A331242 a(n) = number of triangles with integer sides i <= j <= k with radius of enclosing circle <= n.

1, 8, 26, 56, 106, 175, 272, 397, 555, 750

Offset

1,2

Comments

The enclosing circle differs from the circumcircle by limiting the radius to (longest side)/2 for obtuse triangles, i.e., those with i^2 + j^2 < k^2.

Links

Table of n, a(n) for n=1..10.

Example

The list of radii of the n-th enclosing circle, rounded to 10^-4, starts: {0.57735, 1.0328, 1.1547, 1.5000, 1.5213, 1.5910, 1.7321, 2.0000, 2.0125, 2.0158, 2.0656, 2.1574, 2.3094, 2.5000, 2.5000, 2.5000, 2.5126, 2.5516, 2.5621, 2.6207, 2.7277, 2.8868, 3.0000, 3.0000, 3.0000, 3.0000, 3.0105, ...}.
a(1) = 1: 1 circle (R = 0.57735) with R <= 1,
a(2) = 8: a(1) + 7 circles (R = 1.0328, 1.1547, 1.5000, 1.5213, 1.5910, 1.7321, 2.0000) with 1 < R <= 2,
a(3) = 26: a(2) + 18 circles (R = 2.0125, 2.0158, 2.0656, 2.1574, 2.3094, 2.5000, 2.5000, 2.5000, 2.5126, 2.5516, 2.5621, 2.6207, 2.7277, 2.8868, 3.0000, 3.0000, 3.0000, 3.0000) with 2 < R <= 3.

Crossrefs

Cf. A331229, A331240, A331243, A331244, A331245, A331246.

Sequence in context: A085690 A005897 A215097 * A111694 A129111 A002413

Adjacent sequences: A331239 A331240 A331241 * A331243 A331244 A331245

Keyword

nonn,more

Author

Hugo Pfoertner, Jan 20 2020

Status

approved